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dc.contributor.advisorSantos Leal, Francisco 
dc.contributor.authorBlanco Gómez, Mónica 
dc.contributor.otherUniversidad de Cantabriaes_ES
dc.description.abstractABSTRACT: We study the enumeration of d-dimensional lattice polytopes with n lattice points, for fixed d and n>d. - We prove that in each dimension d there is a constant w(d) such that: for each n>d there exist only finitely many d-dimensional lattice polytopes with n lattice points and lattice width strictly larger than w(d). We show that w(4)=2. - In dimension 3 we develop an algorithm that enumerates the (finite) list of 3-dimensional lattice polytopes with n lattice points and lattice width strictly larger than 1, from the (finite) list of those with n-1 lattice points. We include codes that implement the algorithm in MATLAB, with which we have computed the lists of the polytopes with up to 11 lattice points.es_ES
dc.description.abstractRESUMEN: Estudiamos la enumeración de politopos reticulares d-dimensionales con n puntos reticulares, para d y n>d fijados. - Demostramos que en cada dimensión d existe una constante w(d) tal que: para cada n>d existe sólo un número finito de politopos reticulares d-dimensionales con n puntos reticulares y anchura reticular estrictamente mayor que w(d). Se demuestra que w(4)=2. - En dimensión 3 elaboramos un algoritmo que calcula la lista (finita) de politopos reticulares 3-dimensionales con n puntos reticulares y de anchura reticular estrictamente mayor que 1, a partir de la lista (finita) de los que tienen n-1 puntos reticulares. Se adjuntan códigos que implementan dicho algoritmo en MATLAB, y con los que se han calculado las listas de dichos politopos con hasta 11 puntos reticulares.es_ES
dc.description.sponsorshipThis thesis has been developed under the following scholarships and project grants of the Spanish Ministry of Economics and Competitiveness: MTM2011-22792 and MTM2014-54207-P; BES-2012-058920; EEBB-I-2014-08588 and EEBB-I-2016-10623. I also need to thank The European Science Foundation within the ACAT Project, for partially funding my research visit in Berlin.es_ES
dc.format.extent194 p.es_ES
dc.rightsAtribución-NoComercial-CompartirIgual 3.0 España*
dc.subject.otherGeometría discretaes_ES
dc.subject.otherPolitopos reticulareses_ES
dc.subject.otherAnchura reticulares_ES
dc.subject.otherPuntos reticulareses_ES
dc.subject.otherDiscrete geometryes_ES
dc.subject.otherLattice polytopeses_ES
dc.subject.otherLattice widthes_ES
dc.subject.otherLattice pointses_ES
dc.titleEnumeration and width of lattice polytopes by their number of lattice pointses_ES
dc.title.alternativeEnumeración y anchura de politopos reticulares por su número de puntos reticulareses_ES

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Atribución-NoComercial-CompartirIgual 3.0 EspañaExcept where otherwise noted, this item's license is described as Atribución-NoComercial-CompartirIgual 3.0 España